Filter spaces: towards a unified theory of large cardinal and embedding axioms
نویسندگان
چکیده
منابع مشابه
Tameness from Large Cardinal Axioms
We show that Shelah’s Eventual Categoricity Conjecture follows from the existence of class many strongly compact cardinals. This is the first time the consistency of this conjecture has been proven. We do so by showing that every AEC with LS(K) below a strongly compact cardinal κ is < κ tame and applying the categoricity transfer of Grossberg and VanDieren [GV06a]. These techniques also apply t...
متن کاملLarge Cardinal Axioms from Tameness in Aecs
We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions. For instance, we show: Theorem. Let κ be uncountable such that μω < κ for every μ < κ. If every AEC with Löwenheim-Skolem number less than κ is < κ-tame, then κ is almost strongly compact. This is done by isolating a class of AECs that exh...
متن کاملForcing Axioms and Cardinal Arithmetic
We survey some recent results on the impact of strong forcing axioms such as the Proper Forcing Axiom PFA and Martin’s Maximum MM on cardinal arithmetic. We concentrate on three combinatorial principles which follow from strong forcing axioms: stationary set reflection, Moore’s Mapping Reflection Principle MRP and the P-ideal dichotomy introduced by Abraham and Todorčević which play the key rol...
متن کاملTOWARDS THE THEORY OF L-BORNOLOGICAL SPACES
The concept of an $L$-bornology is introduced and the theory of $L$-bornological spacesis being developed. In particular the lattice of all $L$-bornologies on a given set is studied and basic properties ofthe category of $L$-bornological spaces and bounded mappings are investigated.
متن کاملBASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES
Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1989
ISSN: 0168-0072
DOI: 10.1016/0168-0072(89)90009-2